List questions from entire-functions

Published on 07 Jan 2024 - 19:03

77

Views

Let $f,g$ entire functions both $\neq 0$ such that $|f|^2\leq |g|^3$, what can we say about their zeroes?

Published on 10 Jan 2024 - 14:29

89

Views

If $f(z)=e^z$ then $f(A)=?$...

Published on 03 Feb 2024 - 8:15

208

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Entire function bounded in every horizontal line, and has limit along the positive real line

Published on 06 Feb 2024 - 20:37

45

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Show that any entire function satisfying the given conditions is a constant.

Published on 09 Feb 2024 - 13:23

76

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Find all entire functions such that $|f(z+z')|\leq |f(z)| + |f(z')|$, for all $z,z'\in\mathbb{C}$

Published on 23 Mar 2024 - 7:28

36

Views

Entire function maps bounded sets to bounded sets

Published on 30 Mar 2024 - 13:57

8.9k

Views

Proving that a doubly-periodic entire function $f$ is constant.

Published on 26 Mar 2026 - 17:31

116

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$f$ is an entire function and there are $a,b$ such that $f(z+w_1)=af(z)$ and $f(z+w_2)=bf(z)$. Show that $f=Ae^{Bz}$.

Published on 06 May 2015 - 15:30

463

Views

Show that $f$ is a polynomial

Published on 23 Mar 2026 - 0:38

109

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Show that $b_n=0$

Published on 26 Mar 2026 - 16:15

466

Views

Identity theorem - entire function

Published on 19 Mar 2016 - 20:41

1.8k

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Any entire function without zero is constant

Published on 25 Mar 2016 - 21:26

112

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Does there exist such analytic function?

Published on 27 Mar 2016 - 6:28

548

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Entire function bounded by logarithm

Published on 07 Apr 2016 - 12:14

List Question

Existence or non-existence of an entire funtion

Let $f,g$ entire functions both $\neq 0$ such that $|f|^2\leq |g|^3$, what can we say about their zeroes?

If $f(z)=e^z$ then $f(A)=?$...

Entire function bounded in every horizontal line, and has limit along the positive real line

Show that any entire function satisfying the given conditions is a constant.

Find all entire functions such that $|f(z+z')|\leq |f(z)| + |f(z')|$, for all $z,z'\in\mathbb{C}$

Entire function maps bounded sets to bounded sets

Proving that a doubly-periodic entire function $f$ is constant.

$f$ is an entire function and there are $a,b$ such that $f(z+w_1)=af(z)$ and $f(z+w_2)=bf(z)$. Show that $f=Ae^{Bz}$.

Show that $f$ is a polynomial

Show that $b_n=0$

Identity theorem - entire function

Any entire function without zero is constant

Does there exist such analytic function?

Entire function bounded by logarithm

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